The present invention relates to a fuel element for a reactor, especially for a gas cooled nuclear reactor, with roughness elements on the surface of the cladding tube in order to improve the heat transfer between that surface and the coolant surrounding it.
It is a well known fact (Proceedings of the 1970 Heat Transfer and Fluid Mechanics Institute, Stanford, California, pp. 354-370) that roughnesses (elevations on a surface influencing only the boundary layer of a flow) can improve the heat transfer between the cladding surface of a fuel element and the coolant. At the same time, however, this measure will also enhance the pressure drop in the coolant duct.
It is also known from the same publication and another one (Druckverlust und Warmeubergang an glatten und rauhen Flachen, External Report No. 4/71-29, Karlsruhe Nuclear Research Center) that every roughness is characterized by a specific quantity, the so called roughness function, R (h.sup.+). "Roughness elements" are elevations on a surface which influence only the boundary layer of the coolant flow. This means that the ratio between the height of the roughness and the hydraulic diameter should be below 0.02. If this roughness function is known, the friction coefficient of a specific geometric arrangement, e.g., a bundle of roughened rods of the type used in a gas cooled reactor, can be calculated for a defined roughness.
It can also be taken from these publications that a low value of R (h.sup.+ ) results in a high friction coefficient with the heat transfer coefficient rising at the same time.
Since the pressure drop is directly proportional to the circulator power, the ratio between the improvement in heat transfer and the increase in the pressure drop determines any optimization of a circuit of a gas cooled reactor.
The following calculation clearly shows these conditions. The terms and quantities have the following meanings:
Q = power transferred from the fuel element pins to the coolant PA1 .DELTA. T = temperature difference between the wall and the coolant PA1 m = mass flow PA1 h = heat transfer coefficient PA1 U = circumference of fuel element pins PA1 L = free cross section PA1 .rho. = density PA1 cp = specific heat PA1 f = friction coefficient ##EQU1## D.sub.H = HYDRAULIC DIAMETER ##EQU2## u = mean velocity .DELTA.P = PRESSURE DROP ##EQU3## From the definition of the St-number ##EQU4## and the heat transfer coefficient ##EQU5## we obtain ##EQU6## Substituting Eq. (5) in Eq. (2) results in this relation: ##EQU7## For a given power of the reactor (Q), coolant (.rho., cp), temperature difference (.DELTA. T) and dimensions of the fuel pins (U,L), the pumping power is ##EQU8## Consequently, that roughness is optimal which supplies the lowest ratio of f/St.sup.3.
Usually, the values of the friction coefficient f and the heat transfer ratio St are referred to the corresponding values (i.e., at the same Re number) of a smooth surface. This will directly indicate the factor by which the two quantities have changed.
Normally, the roughness elements consist of circumferential fins made by cutting of the tubes. The improvement in heat transfer and the increase in the pressure drop is a function of the P/h ratio of the roughness, the optimum being at a P/h = 7-10 (P = distance of the roughness elements, h = roughness height). For this type of roughness the minimum roughness parameter is found to be R (h.sup.+) = 3.0.
Locally, there is a very steep rise in the local heat transfer coefficient at the leading edge of an elevation of the roughness elements. According to measurements by means of mass transfer the local increase in heat transfer can be up to three times higher than the mean value. On the other hand, the local heat transfer coefficient decreases sharply downstream of an elevation in the so-called "dead water region" and rises again after a certain distance (approximately four times the height) as a consequence of the turbulences created by the fin. These two counteracting effects will significantly improve the heat transfer coefficient only at major distances between fins.